There have been remarkable advances in imaging technology, used routinely and pervasively in many human studies, that non-invasively measures human brain structure and function. Diffusion magnetic resonance imaging (dMRI) and structural MRI (sMRI) are used to infer locations of millions of interconnected white matter fiber tracts-known as the brain connectome-that act as highways for neural activity and communication across the brain. Evidence is increasing that an individual's brain connectome plays a fundamental role in cognitive functioning, behavior, and the risk of developing mental health and neuropsychiatric disorders. Improved mechanistic understanding of relationships between brain connectome structure and phenotypes and exposures has the potential to revolutionize prevention and treatment of mental health disorders. However, large gaps between the state of the art in image acquisition and in connectome construction and data analysis have limited progress. This project develops a transformative toolbox of data processing and analysis methods for better construction, representation, and analysis of human brain connectomes. These tools will be applied to the Human Connectome Project and UK Biobank datasets, to enhance understanding of how the brain connectome varies according to individual traits and exposures and with neuropsychiatric conditions. The toolbox will be rigorously validated, including assessments of reproducibility and discriminative ability based on scan-rescan data, out-of-sample predictive performance, power and type I error rates in simulation studies, and mechanistic interpretability of the results. There are four Specific Aims: (1) Geometric reconstruction of connectomes to reduce measurement errors and enhance robustness, reproducibility and discriminative power; (2) Geometric representation of connectomes characterizing connectomes in novel ways to encode much more information than is available in typical adjacency matrix representations that rely on a single measure of connection strength between pre-specified regions of interest; (3) Relating connectomes to human traits through new multiscale models and algorithms that improve power and mechanistic insight in statistical analyses relating brain connectomes to phenotypes (cognitive functioning, behavior, mental health conditions), exposures (substance use), and covariates (age, gender); (4) Dissemination of publicly available, well-documented software for routine implementation of the proposed toolbox.